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Magnetic Force
PH 203
Professor Lee Carkner
Lecture 16
Charge Carriers
 Imaging a current flowing from
top to bottom in a wire, with a
magnetic field pointing “in”

 If the charge carriers are negative
(moving to the top), the magnetic
field will also deflect them to the
right
The Hall Effect

If it is high the carriers are
positive

Since a voltmeter shows the
low potential is on the right,
the electron is negative
Hall Quantified

Electrons are now longer deflected and the
potential across the strip is constant

but the velocity is the drift speed of the electrons
v = i/neA

n = Bi/eAE
Since the potential V = Ed and the thickness of
the strip (lower case “ell”), l = A/d
n = Bi/Vle
Electric and Magnetic Force

For a uniform field, electric force vector does not
change

Electric fields accelerate particles, magnetic
fields deflect particles
Particle Motion
A particle moving freely in a magnetic field will
have one of three paths, depending on q
Straight line
When q =
Circle
When q =
Helix
When
This assumes a uniform field that the particle
does not escape from
Circular Motion
Circular Motion

This will change the direction of v, and change the
direction of F towards more bending

How big is the circle?
Magnetic force is F =
Centripetal force is F =
We can combine to get
r = mv/qB
Radius of orbit of charged particle in a uniform
magnetic field
Circle Properties
Circle radius is inversely proportional to q and B

r is directly proportional to v and m

Can use this idea to make mass spectrometer

Send mixed atoms through the B field and they will
come out separated by mass
Helical Motion

Charged particles will spiral around magnetic
field lines
If the field has the right geometry, the particles can
become trapped

Since particles rarely encounter a field at exactly 0
or 90 degrees, such motion is very common
Examples:

Gyrosynchrotron radio emission from planets and stars
Helical
Motion
Magnetic Field and Current

We know that i = q/t and v = L/t (where L is
the length of the wire)
So qv = iL, thus:
F = BiL sin f

We can use the right hand rule to get the
direction of the force
Use the direction of the current instead of v
Force on a
Wire
Force on a Loop of Wire

Consider a loop of wire placed so that it is
lined up with a magnetic field

Two sides will have forces at right angles to
the loop, but in opposite directions
The loop will experience a torque
Loop of Current
Torque on Loop

Since q = 90 and L = h,
F = Bih
The torque is the force times the moment arm
(distance to the center), which is w/2

but hw is the area of the loop, A
t = iBA

t = iBA sin q
Torque on Loop
General Loops

t = iBAN sin q
The torque is maximum when the loop is aligned
with the field and zero when the field is at right
angles to the loop (field goes straight through loop)

 If you reverse the direction of the current at just
the right time you can get the coil to spin
Can harness the spin to do work

Next Time
Read 29.1-29.4
Problems: Ch 28, P: 22, 36, 67, Ch 29, P:
1, 27
Test 2 next Friday
A beam of electrons is pointing right at you.
What direction would a magnetic field have
to have to produce the maximum deflection
in the right direction?
A)
B)
C)
D)
E)
Right
Left
Up
Down
Right at you
A beam of electrons is pointing right at you.
What direction would a magnetic field have
to have to produce the maximum deflection
in the up direction?
A)
B)
C)
D)
E)
Right
Left
Up
Down
Right at you
A beam of electrons is pointing right at you.
What direction would a magnetic field have
to have to produce no deflection?
A)
B)
C)
D)
E)
Right
Left
Up
Down
Right at you